{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pole-Zero (PZ) simulation example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this short example we will simulate a simple [RLC circuit](https://en.wikipedia.org/wiki/RLC_circuit) with the [ahkab](https://ahkab.github.io/ahkab/) simulator.\n",
    "\n",
    "In particular, we consider a series resonant RLC circuit. If you need to refresh your knowledge on 2nd filters, you may [take a look at this page](http://hyperphysics.phy-astr.gsu.edu/hbase/electric/serres.html).\n",
    "\n",
    "## The plan: what we'll do\n",
    "\n",
    "### 0. A brief analysis of the circuit\n",
    "\n",
    "This should be done with pen and paper, we'll just mention the results. The circuit is pretty simple, feel free to skip if you find it boring.\n",
    "\n",
    "### 1. How to describe the circuit with ahkab\n",
    "\n",
    "We'll show this:\n",
    "\n",
    "* from Python,\n",
    "* and briefly with a netlist deck.\n",
    "\n",
    "### 2. Pole-zero analysis\n",
    "\n",
    "* We will extract poles and zeros.\n",
    "* We'll use them to build input-output transfer function, which we evaluate.\n",
    "\n",
    "### 3. AC analysis\n",
    "\n",
    "* We will run an AC analysis to evaluate numerically the transfer function.\n",
    "\n",
    "### 4. Symbolic analysis\n",
    "\n",
    "* We'll finally run a symbolic analysis as well.\n",
    "* Once we have the results, we'll substitute for the real circuit values and verify both AC and PZ analysis.\n",
    "\n",
    "### 5. Conclusions\n",
    "\n",
    "We will check that the three PZ, AC and Symbolic analysis match!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The circuit\n",
    "\n",
    "The circuit we simulate is a very simple one:\n",
    "\n",
    "INSERT\n",
    "\n",
    "## 0. Theory\n",
    "\n",
    "Once one proves that the current flowing in the only circuit branch in the Laplace domain is given by:\n",
    "\n",
    "$$I(s) = \\frac{1}{L}\\cdot\\frac{s}{s^2 + 2\\alpha\\cdot s + \\omega_0^2}$$\n",
    "\n",
    "Where:\n",
    "\n",
    "* $s$ is the Laplace varible, $s = \\sigma + j \\omega$:\n",
    "    * $j$ is the imaginary unit,\n",
    "    * $\\omega$ is the angular frequency (units rad/s).\n",
    "* $\\alpha$ is known as the *Neper frequency* and it is given by $R/(2L)$,\n",
    "* $\\omega_0$ is the *(undamped) resonance frequency, equal to $(\\sqrt{LC})^{-1}$.\n",
    "\n",
    "It's easy to show that the pass-band transfer function we consider in our circuit, $V_{OUT}/V_{IN}$, has the expression:\n",
    "\n",
    "$$H(s) = \\frac{V_{OUT}}{V_{IN}}(s) = k_0 \\cdot\\frac{s}{s^2 + 2\\alpha\\cdot s + \\omega_0^2}$$\n",
    "\n",
    "Where the coeffiecient $k_0$ has value $k_0 = R/L$.\n",
    "\n",
    "Solving for poles and zeros, we get:\n",
    "\n",
    "* One zero:\n",
    "    * $z_0$, located in the origin.\n",
    "* Two poles, $p_0$ and $p_1$:\n",
    "    * $p_{0,1} = - \\alpha \\pm \\sqrt{\\alpha^2 - \\omega_0^2}$\n",
    "\n",
    "## 1. Describe the circuit with ahkab\n",
    "\n",
    "Let's call `ahkab` and describe the circuit above.\n",
    "\n",
    "First we need to import `ahkab`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "figsize = (10, 7)\n",
    "# libraries we need\n",
    "import ahkab"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We're using ahkab 0.16\n"
     ]
    }
   ],
   "source": [
    "print \"We're using ahkab %s\" % ahkab.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create a new circuit object titled 'RLC bandpass', which we name `bpf` from Band-Pass Filter:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bpf = ahkab.Circuit('RLC bandpass')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A circuit is made of, internally, components and nodes. For now, our `bpf` circuit is empty and really of not much use.\n",
    "\n",
    "We wish to define our nodes, our components, specifying their connection to the appropriate nodes and inform the circuit instance about the what we did.\n",
    "\n",
    "It sounds complicated, but it is actually very simple, also thanks to the convenience functions `add_*()` in the `Circuit` instances ([circuit documentation](https://ahkab.readthedocs.org/en/latest/circuit.html)).\n",
    "\n",
    "We now add the inductor `L1`, the capacitor `C1`, the resistor `R1` and the input source `V1`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "bpf = ahkab.Circuit('RLC bandpass')\n",
    "bpf.add_inductor('L1', 'in', 'n1', 1e-6)\n",
    "bpf.add_capacitor('C1', 'n1', 'out', 2.2e-12)\n",
    "bpf.add_resistor('R1', 'out', bpf.gnd, 13)\n",
    "# we also give V1 an AC value since we wish to run an AC simulation\n",
    "# in the following\n",
    "bpf.add_vsource('V1', 'in', bpf.gnd, dc_value=1, ac_value=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that:\n",
    "* the nodes to which they get connected (`'in'`, `'n1'`, `'out'`...) are nothing but strings. If you prefer handles, you can call the `create_node()` method of the circuit instance `bpf` ([create_node documentation](https://ahkab.readthedocs.org/en/latest/circuit.html#ahkab.circuit.Circuit.create_node).\n",
    "* Using the convenience methods `add_*`, the nodes are not explicitely added to the circuit, but they are in fact automatically taken care of behind the hood."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have successfully defined our circuit object `bpf`.\n",
    "\n",
    "Let's see what's in there and generate a netlist:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "* RLC bandpass\n",
      "L1 in n1 1e-06\n",
      "C1 n1 out 2.2e-12\n",
      "R1 out 0 13\n",
      "V1 in 0 type=vdc value=1 vac=1 \n"
     ]
    }
   ],
   "source": [
    "print(bpf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above text defines the same circuit in netlist form. It has the advantage that it's a very coincise piece of text and that the syntax resembles (not perfectly yet) that of simulators such as [SPICE](https://newton.ex.ac.uk/teaching/CDHW/Electronics2/userguide/).\n",
    "\n",
    "If you prefer to run `ahkab` from the command line, be sure to check the [Netlist syntax doc page](https://ahkab.readthedocs.org/en/latest/help/Netlist-Syntax.html) and to add the simulation statements, which are missing above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. PZ analysis\n",
    "\n",
    "The analysis is set up easily by calling `ahkab.new_pz()`. Its signature is:\n",
    "\n",
    "    ahkab.new_pz(input_source=None, output_port=None, shift=0.0, MNA=None, outfile=None, x0=u'op', verbose=0)\n",
    "    \n",
    "And you can find [the documentation for ahkab.new_pz here](https://ahkab.readthedocs.org/en/latest/ahkab.html#ahkab.ahkab.new_pz).\n",
    "    \n",
    "We will set:\n",
    "* Input source and output port, to enable the extraction of the zeros.\n",
    "    * the input source is `V1`,\n",
    "    * the output port is defined between the output node `out` and ground node (`bpf.gnd`).\n",
    "* We need no linearization, since the circuit is linear. Therefore we set `x0` to `None`.\n",
    "* I inserted a non-zero shift in the initial calculation frequency below. You may want to fiddle a bit with this value, the algorithm internally tries to kick the working frequency away from the exact location of the zeros, since we expect a zero in the origin, we help the simulation find the zero quickly by shifting away the initial working point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pza = ahkab.new_pz('V1', ('out', bpf.gnd), x0=None, shift=1e3)\n",
    "r = ahkab.run(bpf, pza)['pz']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are in the `pz_solution` object `r`. It has an interface that works like a dictionary.\n",
    "\n",
    "Eg. you can do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[u'p0', u'p1', u'z0']"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r.keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check out the [documentation on pz_solution for more](https://ahkab.readthedocs.org/en/latest/results.html#ahkab.results.pz_solution).\n",
    "\n",
    "Let's see what we got:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Singularities:\n",
      "* p0 = -1.03451e+06 -1.07297e+08j Hz\n",
      "* p1 = -1.03451e+06 +1.07297e+08j Hz\n",
      "* z0 = -1.44751e-13 +0j Hz\n"
     ]
    }
   ],
   "source": [
    "print('Singularities:')\n",
    "for x, _ in r:\n",
    "    print \"* %s = %+g %+gj Hz\" % (x, np.real(r[x]), np.imag(r[x]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note that the results are frequencies expressed in Hz** (and *not* angular frequencies in rad/s).\n",
    "\n",
    "Graphically, we can see better where the singularities are located:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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phWo1breua5GkNjjEadDMrUydjcDqMb6+mTg1Ym9RG7buugBJWkFf67oASWqLK3EaNHMr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\n6iGHOA2auRWNyEycGrG3qA0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d65e490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=figsize)\n",
    "# plot o's for zeros and x's for poles\n",
    "for x, v in r:\n",
    "    plot(np.real(v), np.imag(v), 'bo'*(x[0]=='z')+'rx'*(x[0]=='p'))\n",
    "# set axis limits and print some thin axes\n",
    "xm = 1e6\n",
    "xlim(-xm*10., xm*10.)\n",
    "plot(xlim(), [0,0], 'k', alpha=.5, lw=.5)\n",
    "plot([0,0], ylim(), 'k', alpha=.5, lw=.5)\n",
    "# plot the distance from the origin of p0 and p1\n",
    "plot([np.real(r['p0']), 0], [np.imag(r['p0']), 0], 'k--', alpha=.5)\n",
    "plot([np.real(r['p1']), 0], [np.imag(r['p1']), 0], 'k--', alpha=.5)\n",
    "# print the distance between p0 and p1\n",
    "plot([np.real(r['p1']), np.real(r['p0'])], [np.imag(r['p1']), np.imag(r['p0'])], 'k-', alpha=.5, lw=.5)\n",
    "# label the singularities\n",
    "text(np.real(r['p1']), np.imag(r['p1'])*1.1, '$p_1$', ha='center', fontsize=20)\n",
    "text(.4e6, .4e7, '$z_0$', ha='center', fontsize=20)\n",
    "text(np.real(r['p0']), np.imag(r['p0'])*1.2, '$p_0$', ha='center', va='bottom', fontsize=20)\n",
    "xlabel('Real [Hz]'); ylabel('Imag [Hz]'); title('Singularities');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, we got two complex conjugate poles and a zero in the origin.\n",
    "\n",
    "#### The resonance frequency\n",
    "\n",
    "Let's check that indeed the (undamped) resonance frequency $f_0$ has the expected value from the theory.\n",
    "\n",
    "It should be:\n",
    "\n",
    "$$f_0 = \\frac{1}{2\\pi\\sqrt{LC}}$$\n",
    "\n",
    "Since we have little damping, $f_0$ is very close to the damped resonant frequency in our circuit, given by the absolute value of the imaginary part of either $p_0$ or $p_1$.\n",
    "\n",
    "In fact, the damped resonant frequency $f_d$ is given by:\n",
    "\n",
    "$$f_d = \\frac{1}{2\\pi}\\sqrt{\\alpha^2 -w_0^2}$$\n",
    "\n",
    "Since this is an example and we have Python at our fingertips, we'll compensate for the frequency pulling due to the damping anyway. That way, the example is analytically correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resonance frequency from analytic calculations: 1.07302e+08 Hz\n"
     ]
    }
   ],
   "source": [
    "C = 2.2e-12\n",
    "L = 1e-6\n",
    "f0 = 1./(2*np.pi*np.sqrt(L*C))\n",
    "print 'Resonance frequency from analytic calculations: %g Hz' %f0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resonance frequency from PZ analysis: 1.07292e+08 Hz\n"
     ]
    }
   ],
   "source": [
    "alpha = (-r['p0']-r['p1'])/2\n",
    "a1 = np.real(abs(r['p0'] - r['p1']))/2\n",
    "f0 = np.sqrt(a1**2 - alpha**2)\n",
    "f0 = np.real_if_close(f0)\n",
    "print 'Resonance frequency from PZ analysis: %g Hz' %f0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's alright.\n",
    "\n",
    "## 3. AC analysis\n",
    "\n",
    "Let's perform an AC analysis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "aca = ahkab.new_ac(start=1e8, stop=5e9, points=5e2, x0=None)\n",
    "rac = ahkab.run(bpf, aca)['ac']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we use sympy to assemble the transfer functions from the singularities we got from the PZ analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sympy\n",
    "sympy.init_printing()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy.abc import w\n",
    "from sympy import I\n",
    "p0, p1, z0 = sympy.symbols('p0, p1, z0')\n",
    "k = 13/1e-6 # constant term, can be calculated to be R/L\n",
    "H = 13/1e-6*(I*w + z0*6.28)/(I*w +p0*6.28)/(I*w + p1*6.28)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Hl = sympy.lambdify(w, H.subs({p0:r['p0'], z0:abs(r['z0']), p1:r['p1']}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need a function to evaluate the absolute value of a transfer function in decibels.\n",
    "\n",
    "Here it is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def dB20(x):\n",
    "    return 20*np.log10(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we can plot $|H(\\omega)|$ in dB and inspect the results visually."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JX5U0WdLW/K4KQNiQOQMQJtGi+0lzqqZeMfvCKZeMG6U8t89IZt0DC5xzkSfe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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ed9b410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=figsize)\n",
    "semilogx(rac.get_x()/2/np.pi, dB20(abs(rac['vout'])), label='TF from AC analysis')\n",
    "semilogx(rac.get_x()/2/np.pi, dB20(abs(Hl(rac.get_x()))), 'o', ms=4, label='TF from PZ analysis')\n",
    "legend(); xlabel('Frequency [Hz]'); ylabel('|H(w)| [dB]'); xlim(4e7, 3e8); ylim(-50, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## 4. Symbolic analysis\n",
    "\n",
    "Next, we setup and run a symbolic analysis. \n",
    "\n",
    "We set the input source to be `'V1'`, in this way, `ahkab` will calculate all transfer functions, together with low-frequency gain, poles and zeros, with respect to *every* variable in the circuit.\n",
    "\n",
    "It is done very similarly to the previous cases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "symba = ahkab.new_symbolic(source='V1')\n",
    "rs, tfs = ahkab.run(bpf, symba)['symbolic']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how to the `'symbolic'` key corresponds a tuple of two objects: the symbolic results and the TF object that was derived from it.\n",
    "\n",
    "Let's inspect their contents:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Symbolic simulation results for 'RLC bandpass' (netlist None).\n",
      "Run on 2015-05-07 04:24:42.\n",
      "I[L1]\t = C1*V1*s/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "I[V1]\t = -C1*V1*s/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "VIN\t = V1\n",
      "VN1\t = V1*(C1*R1*s + 1.0)/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "VOUT\t = C1*R1*V1*s/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(rs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Symbolic transfer function results for 'RLC bandpass' (netlist None).\n",
      "Run on 2015-05-07 04:24:42.\n",
      "I[L1]/V1:\n",
      "\tgain:\tC1*s/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "\tgain0:\t0\n",
      "\tpoles:\n",
      "\t\t0.5*(-C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\t\t-0.5*(C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\tzeros:\n",
      "\t\t0\n",
      "I[V1]/V1:\n",
      "\tgain:\t-C1*s/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "\tgain0:\t0\n",
      "\tpoles:\n",
      "\t\t0.5*(-C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\t\t-0.5*(C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\tzeros:\n",
      "\t\t0\n",
      "VIN/V1:\n",
      "\tgain:\t1\n",
      "VN1/V1:\n",
      "\tgain:\t(C1*R1*s + 1.0)/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "\tgain0:\t1.00000000000000\n",
      "\tpoles:\n",
      "\t\t0.5*(-C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\t\t-0.5*(C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\tzeros:\n",
      "\t\t-1/(C1*R1)\n",
      "VOUT/V1:\n",
      "\tgain:\tC1*R1*s/(C1*L1*s**2 + C1*R1*s + 1.0)\n",
      "\tgain0:\t0\n",
      "\tpoles:\n",
      "\t\t0.5*(-C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\t\t-0.5*(C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)\n",
      "\tzeros:\n",
      "\t\t0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print tfs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In particular, to our transfer function corresponds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{u'gain': C1*R1*s/(C1*L1*s**2 + C1*R1*s + 1.0),\n",
       " u'gain0': 0,\n",
       " u'poles': [0.5*(-C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1),\n",
       "  -0.5*(C1*R1 + sqrt(C1*(C1*R1**2 - 4.0*L1)))/(C1*L1)],\n",
       " u'zeros': [0]}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tfs['VOUT/V1']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's easy to show the above entries are a different formulation that corresponds to the theoretical results we introduced at the beginning of this example.\n",
    "\n",
    "We'll do it graphically. First of all, let's isolate out TF:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMsAAAAtBAMAAADyyIKfAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
      "text/latex": [
       "$$\\frac{C_{1} R_{1} s}{C_{1} L_{1} s^{2} + C_{1} R_{1} s + 1.0}$$"
      ],
      "text/plain": [
       "        C₁⋅R₁⋅s         \n",
       "────────────────────────\n",
       "       2                \n",
       "C₁⋅L₁⋅s  + C₁⋅R₁⋅s + 1.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Hs = tfs['VOUT/V1']['gain']\n",
    "Hs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We wish to substitute the correct circuit values to `R1`, `L1` and `C1` to be able to evaluate numerically the results.\n",
    "\n",
    "In order to do so, the `symbolic_solution` class in the `results` module has a method named `as_symbols` that takes a string of space-separed symbol names and returns the `sympy` symbols associated with them ([symbolic_solution.as_symbols documentation](https://ahkab.readthedocs.org/en/latest/results.html#ahkab.results.symbolic_solution.as_symbols))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "s, C1, R1, L1 = rs.as_symbols('s C1 R1 L1')\n",
    "HS = sympy.lambdify(w, Hs.subs({s:I*w, C1:2.2e-12, R1:13., L1:1e-6}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Did we get the same results, let's sat within a 1dB accuracy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.allclose(dB20(abs(HS(rac.get_x()))), dB20(abs(Hl(rac.get_x()))), atol=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good.\n",
    "\n",
    "## 5. Conclusions\n",
    "\n",
    "Let's take a look at PZ, AC and symbolic results together:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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iHxORp0TkERF5BcBKEXmPiGwTkR3m2DJz/kVm389E5GUR2SoiK0XkYZPNeyJR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e2ed590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=figsize);  title('Series RLC passband: TFs compared')\n",
    "semilogx(rac.get_x()/2/np.pi, dB20(abs(rac['vout'])), label='TF from AC analysis')\n",
    "semilogx(rac.get_x()/2/np.pi, dB20(abs(Hl(rac.get_x()))), 'o', ms=4, label='TF from PZ analysis')\n",
    "semilogx(rac.get_x()/2/np.pi, dB20(abs(HS(rac.get_x()))), '-', lw=10, alpha=.2, label='TF from symbolic analysis')\n",
    "vlines(1.07297e+08, *gca().get_ylim(), alpha=.4)\n",
    "text(7e8/2/np.pi, -45, '$f_d = 107.297\\\\, \\\\mathrm{MHz}$', fontsize=20)\n",
    "legend(); xlabel('Frequency [Hz]'); ylabel('|H(w)| [dB]'); xlim(4e7, 3e8); ylim(-50, 1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I hope this example helped show how to use [ahkab](https://ahkab.github.io/ahkab/) and in particular how to perform PZ, AC and symbolic analysis. If it also cleared up some doubts, great!\n",
    "\n",
    "Please remember this is an experimental simulator and you may find bug... it's getting better bu we're not really ready for prime time yet: please report any and all bugs you may encounter on [the issue tracker](https://github.com/ahkab/ahkab/issues)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
